The Constitution,in setting limits on Congress, says in Article One: "The privilege of the Writ of Habeas Corpus shall not be suspended,unless when in Cases of Rebellion or Invasion the public Safety may require it."
VOA: special.2009.02.09
This is the Amazon "Recommendations for you" or Apple "Genius" writ large.
The likelihood of either the CAFC granting en banc consideration or the Supreme Court granting a writ of certiorari is considered by legal experts to be small.